Census records are an important source for British family history research.  They provide a 'snapshot' of the entire population of Britain every 10 years.  They can therefore be used as a source for narrowing down time periods of births, deaths and marriages in families as well as other events such as changes of occupation and family movements.

ENGLAND & WALES 

6 June 1841
30 March 1851
7 April 1861
2 April 1871
3 April 1881
5 April 1891
31 March 1901

Name
Age
(exact age for children under the age of 16 but rounded down to the nearest five years for those older)
Whether or not born in the county

While this is of some use to family historians, the later censuses commencing with that of 1851 are of much more use since they contain, among other information, the following details:

Name
Exact age
Relationship to the head of the household
Occupation
Birthplace

The 1901 census
In 2002, the 1901 census for England & Wales was released for public access by the United Kingdom's National Archives.  The entire census has been indexed by name, the original returns have been digitised and on-line.  It's also worth visiting 1901: Living at the time of the census, which provides useful context to anyone interested in the world their ancestors may have lived in the England and Wales of 1901.

IRELAND 

Censuses were taken in Ireland regularly every 10  years from 1821. However, almost all the census returns for 1821-51 were lost in the fire that destroyed the Public Record Office of Ireland, Four Courts, Dublin, in 1922.   Returns for 1861 and 1871 had already been pulped.  Returns for 1881 and 1891 were used as scrap paper during World War I.  A few of the enumerators' and householders' returns survived the 1922 fire and these are now preserved in the National Archives of Ireland [NAI], formerly Public Record Office.  There are microfilm copies of the Ulster material in the Public Record Office of Northern Ireland [PRONI].  Most of this surviving material is for 1821 and gives names, ages, occupations, relationship to householder of all occupants as well as details of height of house and area of farm.  The religious affiliation is not specified.

1901 and 1911 censuses
The 1901 and 1911 householders' census returns for all Ireland are held in the National Archives of Ireland, Bishop Street, Dublin 8.  But it is all now microfilmed by the LDS Church and can be ordered for viewing through their Family History Libraries.

The 1911 census also provides the important additional information of the number of years married, number of children born and alive.  Be aware that any census taken in the state of Northern Ireland since its establishment in 1921 is subject to a 100 year closure in the same way as the rest of the United Kingdom, so the 1911 census of the six counties of Northern Ireland (Down, Antrim, Armagh, Tyrone, Londonderry, Fermanagh) are not yet released.  The returns for Northern Ireland census of 1926 were apparently destroyed during World War II and those for 1937, 1951, 1961, 1971, 1981 and 1991 are now deposited in PRONI but subject to closure.